Leptin has been considered as a novel treatment for Alzheimer?s disease (AD), but we lack adequate evidence of a biological signal indicative of a therapeutic effect in patients with AD. Some concerns are related to side effects, along with uncertainty about dosing. We will therefore perform a pilot study in patients with AD that is sufficient in scope to assess the impact of Leptin on biomarkers selected for their relevance to the mechanism of action of Leptin and the pathobiology of AD. In addition, the study will help clarify tolerability, safety, and feasibility issues relevant for consideration of a larger subsequent trial. The trial may be used as a stepping-stone to a larger and longer multicenter trial in patients with AD or mild cognitive impairment. 45 patients with mild-moderate probable AD and plasma leptin levels of (</=14 ng/ml) will be randomized to treatment with Leptin at two doses (1 and 5 mg daily) or placebo in a double-blind manner for 12 weeks. The enrollment will target recruitment of 50 patients to achieve a sample of 45 study completers. Spinal taps will be performed at baseline and repeated after 12 weeks of therapy. A final visit will occur 4 weeks after cessation of therapy to assess for possible untoward effects of the Leptin therapy or lumbar puncture.